The next step is to consider the probability \(f(P_i)\)  to get a modality associated with projector \(P_i\) . By construction a context is such that \(\sum _{i=1}^{i=N} P_i = I\) , and \(\sum _{i=1}^{i=N} f(P_i) = 1\)  for any complete set \(\lbrace  P_i \rbrace \) . But these are just the hypothesis of Gleason's theorem [1]}, [2]}, so there is a density matrix \(\rho \)  such that \(f(P_i) = \textrm {Trace}(\rho P_i)\) . If the value 1 is reached, then \(\rho \)  is also a projector \(Q_j\)  and \(f(P_i) = \textrm {Trace}(Q_j P_i )\)  which is the usual Born's formula.
